Uniform convergence of the p-Bieberbach polynomials in domains with zero angles

ABDULLAYEV F., Özkartepe P. N.

Science China Mathematics, cilt.58, sa.5, ss.1063-1078, 2015 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 58 Sayı: 5
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s11425-014-4908-x
  • Dergi Adı: Science China Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1063-1078
  • Anahtar Kelimeler: Bieberbach polynomials, complex approximation, conformal mapping, quasiconformal curve
  • Uşak Üniversitesi Adresli: Hayır

Özet

Let G ⊂ ℂ be a simply connected domain whose boundary L := ∂G is a Jordan curve and 0 ∈ G. Let w = φ(z) be the conformal mapping of G onto the disk B(0, r0) := {w : |w| < r0}, satisfying φ(0) = 0, φ′(0) = 1. We consider the following extremal problem for p > 0: (Formula Presented.) in the class of all polynomials Pn(z) of degree not exceeding n with Pn(0) = 0, Pn′ (0) = 1. The solution to this extremal problem is called the p-Bieberbach polynomial of degree n for the pair (G, 0). We study the uniform convergence of the p-Bieberbach polynomials Bn,p(z) to the φ(z) on (Formula Presented.) with interior and exterior zero angles determined depending on the properties of boundary arcs and the degree of their “touch”.